Asymmetric acessorizing
Normally my opinions on how to dress stylishly are very classic. I would describe my personal style tastes as a blend of classic chic and modern sexy, as in shoots for timelessness with a little more skin than is traditional. I tend to not like anything all that trendy or edgy. But one avant-garde idea I'm interested in and would like to try a little bit more is asymmetric accessorizing. At least in theory, I like the idea of, when considering accessories that tend to be in matched sets, choosing two unmatched that are different from each other in some complimentary way.
Shoes in two different colors. Might be a little tricky to mismatch workably; they would have to be the same height and angle to make walking comfortable. I think I would like this best if the shoes were identical in every way except color, but I could see if you chose carefully enough coordinately differently styled shoes if they complimented each other. Shoes can be great accents, especially in a neutral outfit, so I like the idea of giving them even more pop.
One style of earring in one ear and a different style on the other. Maybe one stud and one dangling made of the same materials. Maybe the same style but in different colors of stone or metal. With the hair worn up to draw attention to the pointed asymmetry.
Eyeshadow that is done one way on the left eye and another way on the right. I don't wear makeup or know much about it, so I'm not sure how you could accomplish this in a way that didn't look exaggerated or even clownish-- might never work for an elegant or everyday look --but I think it could be interesting and remarkable.
I think you'd have to do any of these things carefully and thoughtfully to keep them from looking silly. But I think it could be done in such a way as to look edgy without being too out there.